How to obtain the continued fraction convergents of the number $e$ by neglecting integrals

Published 17 May 2010 in math.NT | (1005.2951v2)

Abstract: In this note, we show that any continued fraction convergent of the number $e = 2.71828...$ can be derived by approximating some integral $I_{n, m} := \int_{0}^{1} xⁿ (1 - x)^m e^x d x$ $(n, m \in \mathbb{N})$ by 0. In addition, we present a new way for finding again the well-known regular continued fraction expansion of $e$.

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Authors (1)

Bakir Farhi

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